Related papers: Wave maps on (1+2)-dimensional curved spacetimes

We study space--time isogeometric discretizations of the linear acoustic wave equation that use splines of arbitrary degree p, both in space and time. We propose a space--time variational formulation that is obtained by adding a…

We prove here essentially sharp linear and bilinear Strichartz type estimates for the wave equations on Minkowski space, where we assume the initial data possesses additional regularity with respect to fractional powers of the usual angular…

We present numerical evidence that singularities form in finite time during the evolution of 2+1 wave maps from spherically equivariant initial data of sufficient energy.

A two-dimensional water wave model based on conformal mapping is presented. The model is exact in the sense that it does not rely on truncated series expansions, nor suffer any numerical diffusion. Additionally, it is computationally highly…

The first article in a two-part series (the second article being [arXiv:2205.13197]) assumes a weak local energy decay estimate holds and proves that solutions to the linear wave equation with variable coefficients in $\mathbb R^{1+3}$,…

The two-sphere valued wave map flow on a Lorentzian domain R x Sigma, where Sigma is any flat two-torus, is studied. The Cauchy problem with initial data tangent to the moduli space of holomorphic maps Sigma -> S^2 is considered, in the…

In this paper we initiate the study of equivariant wave maps from 2d hyperbolic space into rotationally symmetric surfaces. This problem exhibits markedly different phenomena than its Euclidean counterpart due to the exponential volume…

In this paper, we overview the recent progresses on the lifespan estimates of classical solutions of the initial value problems for nonlinear wave equations in one space dimension. There are mainly two directions of the developments on the…

We study a model of internal waves under periodic forcing in an effectively 2-dimensional aquarium. When the underlying classical dynamics has sufficiently irrational rotation number, we prove that the solution to the internal waves…

The group theoretical approach to the relativistic wave equations on the real reducible spaces for spin~0, 1/2 and~1 massless particles is considered. The invariant wave equations which determine the appropriate irreducible representations…

This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and…

Localized energy estimates have become a fundamental tool when studying wave equations in the presence of asymptotically at background geometry. Trapped rays necessitate a loss when compared to the estimate on Minkowski space. A loss of…

We prove global well-posedness of the initial value problem for a class of variational quasilinear wave equations, in one spatial dimension, with initial data that is not-necessarily small. Key to our argument is a form of quasilinear null…

We are interested in the stability of a class of totally geodesic wave maps, as recently studied by Abbrescia and Chen, and later by Duan and Ma. The relevant equations of motion are a system of coupled semilinear wave and Klein-Gordon…

A global weak solution of the biharmonic wave map equation in the energy space for spherical targets is constructed. The equation is reformulated as a conservation law and solved by a suitable Ginzburg-Landau type approximation.

It has been the dominant view for over two decades that all waves are localized in two dimensions for any given amount of disorder. Here, I would like to raise questions about this assertion. The discussion leads to the conclusion that…

We derive the invariant imbedding equations for plane electromagnetic waves propagating in stratified magnetic media, where both dielectric and magnetic permeabilities vary in one spatial direction in an arbitrary manner. These equations…

This paper presents an evaluation of the wave function coefficients for conformally coupled scalars at both one and two-loop levels at leading order in the coupling constant, in momentum space. We take cues from time-dependent interactions…

We study a model of internal waves in an effectively 2D aquarium under periodic forcing. In the case when the underlying classical dynamics has sufficiently irrational rotation number, we prove that the energy of the internal waves remains…

We classify 2+1 dimensional integrable systems with nonlocality of the intermediate long wave type. Links to the 2+1 dimensional waterbag system are established. Dimensional reductions of integrable systems constructed in this paper provide…